Problem: Katie and Tyler are working at their lemonade stand. They have sold $2\dfrac{1}{2}$ pitchers of lemonade and now have $\dfrac13$ of a pitcher left to sell. How many pitchers of lemonade did they start with?
Solution: Katie and Tyler sold $2\dfrac12$ pitchers of lemonade and are left with $\dfrac13$ of a pitcher of lemonade. $2\frac{1}{2}$ $\frac{1}{3}$ pitchers of lemonade to start pitchers sold pitchers left ${2\dfrac12} + \dfrac13}={{?}}$ Our denominators need to be the same so we can add. What is the least common multiple for the denominators $2$ and $3}$ ? The least common multiple of $2$ and $3}$ is ${6}$. $\dfrac{{1}\times 3}{{2}\times 3} = {\dfrac{3}{6}}$ $\dfrac{1}\times 2}{3}\times 2} = \dfrac{2}{6}}$ Now, we can add our fractions. ${2\dfrac{3}{6}} + \dfrac{2}{6}} = 2\dfrac{{3} + 2}}{6} ={2 \dfrac{5}{6}}$ Katie and Tyler started with ${2\dfrac{5}{6}}$ pitchers of lemonade.